Final answer:
The vertex of the given quadratic equation can be found using the formula x_v = -b/(2a). Plugging in the coefficients, we find that the vertex is the point (0, -4).
Step-by-step explanation:
The given quadratic equation is in the standard form, f(p(x)) = -\frac{3}{8}x^2 - 4. To identify the vertex, we can compare the equation to the standard form, which is f(x) = ax^2 + bx + c. By comparing the coefficients, we have a = -\frac{3}{8}, b = 0, and c = -4. The x-value of the vertex, denoted as x_v, can be found using the formula x_v = -\frac{b}{2a}. Plugging in the values, we get x_v = -\frac{0}{2\left(-\frac{3}{8}\right)}. Since the coefficient of b is zero, the x-value of the vertex is simply x_v = 0. To find the y-value of the vertex, denoted as y_v, we substitute the x-value into the equation, giving us y_v = -\frac{3}{8}(0)^2 - 4. Simplifying further, we find that y_v = -4. Therefore, the vertex is the point (0, -4).